In which of these molecules or ions does the presence of nonbonding electron pairs produce an effect on molecular shape? (a) $\mathrm{CO}_{2},(\mathbf{b}) \mathrm{CH}_{2} \mathrm{Br}_{2,}(\mathbf{c}) \mathrm{OF}_{2},(\mathbf{d}) \mathrm{BCl}_{3},(\mathbf{e}) \mathrm{SF}_{6}$

For each molecule, we will first identify the central atom. The central atom is typically the least electronegative element and has the highest valence. In our case, we have: a) CO₂: C is the central atom b) CH₂Br₂: C is the central atom c) OF₂: O is the central atom d) BCl₃: B is the central atom e) SF₆: S is the central atom

Next, we will calculate the number of valence electrons for the central atom in each molecule and count the number of electron groups (lone pairs and bonding pairs) surrounding each central atom: a) CO₂: C has 4 valence electrons + 2 * (2 valence electrons for each O) = 8 valence electrons and 2 electron groups (2 double bonds) b) CH₂Br₂: C has 4 valence electrons + 2 * (1 valence electron for each H) + 2 * (7 valence electrons for each Br) = 20 valence electrons and 4 electron groups (2 single bonds and 2 single bonds) c) OF₂: O has 6 valence electrons + 2 * (7 valence electrons for each F) = 20 valence electrons and 4 electron groups (2 single bonds and 2 lone pairs) d) BCl₃: B has 3 valence electrons + 3 * (7 valence electrons for each Cl) = 24 valence electrons and 3 electron groups (3 single bonds) e) SF₆: S has 6 valence electrons + 6 * (7 valence electrons for each F) = 48 valence electrons and 6 electron groups (6 single bonds)

Now, for each molecule, we will apply the VSEPR Theory to determine the molecular geometry. Take into consideration the electron group geometry as well: a) CO₂: 2 electron groups with no lone pairs give a linear geometry. b) CH₂Br₂: 4 electron groups with no lone pairs give a tetrahedral geometry. c) OF₂: 4 electron groups with 2 lone pairs give a bent geometry. d) BCl₃: 3 electron groups with no lone pairs give a trigonal planar geometry. e) SF₆: 6 electron groups with no lone pairs give an octahedral geometry.

Finally, we will identify which molecules have nonbonding electron pairs that affect their shape: a) CO₂: No lone pairs, linear geometry - No effect b) CH₂Br₂: No lone pairs, tetrahedral geometry - No effect c) OF₂: 2 lone pairs, bent geometry - Effect on molecular shape d) BCl₃: No lone pairs, trigonal planar geometry - No effect e) SF₆: No lone pairs, octahedral geometry - No effect So, only molecule (c) OF₂ has nonbonding electron pairs that produce an effect on the molecular shape.